PLS HELP, finding magnitude of acceleration and tension equations

Question

 Two blocks are connected by a string as shown. The inclination of the ramp is θ = 36° while the masses of the blocks are m₁ = 3.7 kg and m₂ = 16.2 kg. Friction is negligible.

(search question above for diagram)

Write an equation for the magnitude of the acceleration the two blocks experience. Give your equation in terms of m1, m2, θ, and the acceleration due to gravity g. Consider down the ramp to be the negative direction in this calculation.

What is the magnitude of the acceleration of each block in ms2?

Write an equation for the tension in the string in terms of m2, the acceleration due to gravity g, and the acceleration of the two blocks a.

What is the tension in the rope in newtons?

Answer 1

Given

θ = 36°

m₁ = 3.7 kg

m₂ = 16.2 kg

Friction is negligible.

Find

a) Write an equation for the magnitude of the acceleration the two blocks experience. Give your equation in terms of m1, m2, θ, and the acceleration due to gravity g. Consider down the ramp to be the negative direction in this calculation.

b) What is the magnitude of the acceleration of each block in ms2?

c) Write an equation for the tension in the string in terms of m2, the acceleration due to gravity g, and the acceleration of the two blocks a.

d) What is the tension in the rope in newtons?

Solution

Please note: a1 = a2 = a

a)

Mass 1

Sum force X = m1a

T - m1gsinθ = m1a

T = m1a + m1gsinθ Equation 1

Mass 2

Sum force Y = m2a

(Going down in direction of acceleration as positive)

m2g - T = m2a Equation 2

Sub in equation 1 to equation 2

m2g - (m1a + m1gsinθ ) = m2a

a = g(m2-m1sinθ)/(m2+m1)

b)

a = 9.81 (16.2-3.7*sin36)/(16.2+3.7) = 6.91 m/s^2

c) Rewrite equation 2

m2g - T = m2a

T = m2g-m2a = m2(g-a)

d) T = 16.2 (9.81-6.91) = 46.98 N